Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$

Abstract

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A 1 by taking tensor products of irreducibles defined in [7] with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type A 1 , and give sufficient and necessary conditions for these induced modules to be reducible.

Simple Harish-Chandra modules over the super affine-Virasoro algebras

“…The affine-Virasoro algebra is the semi-direct sum of the Virasoro algebra and the untwisted affine Lie algebra. There have been many researches on the representation theory of the affine-Virasoro algebras, see references [7,9,11,16], and so on. However, the research concerning the representation theory of the super affine-Virasoro algebra is still seldom.…”